What is the relationship between the probability of an event's occurrence and the probability that it will not occur?

% chance to occur + % chance to not occur = 100% Expressed in decimals, 40% chance to occur + 60% chance to not occur = 100%. .40 + .60 = 1.00 More detailed answer: === === Probability of event occurrence versus failure to occur First, probabilities are expressed as decimals or fractions with values between zero and one, with zero representing no possibility of an event's occurrence, and one representing the certainty of occurrence. For example, the probability of flipping a heads with one flip of a fair coin is 0.5 or 1/2. The probability of rolling a snake-eye with one roll of one fair die is 0.167 or 1/6. The probability of pulling the Ace of spades out of regular deck of shuffled cards (without the jokers) is 0.0192 or 1/52. The probability of pulling a heart -- any heart -- out of the same deck (assuming the Ace of spades was put back in) is 0.25 or 13/52. Remember, a probability must always be between 0 and 1. If you ever do a probability calculation and get a result greater than one, you screwed up. Second, the probability of any event's failure to occur is one minus the probability of the event's occurrence. So, if the probability of rolling a snake-eye with one fair die is 0.167, then the probability of NOT rolling a snake-eye is 1 - 0.167 = 0.833. (Or 1 - 1/6 = 5/6.) The probability of NOT drawing a heart from a deck of 52 cards is 1 - 0.25 = 0.75. (Or 1 - 1/4 = 3/4). == ==